In this paper we study the dynamics of global attractor of a semilinear parabolic equation involving Grushin operators. First we show that the global attractor is bounded in ${ L^∞(Ω) }$ and ${ D(A) }$. Then we investigate the existence of a Lyapunov function, the injectivity on the global attractor and the squeezing property. Finally, we obtain estimates on upper bound and lower bound of the fractal dimension of the global attractor.